Mathematics questions
18011 published questions with worked solutions.
- If x 1 + x + ^2 x ,dx = x - K A ^ -1 ( K x + 1 A ) + C, (C is a constant of integration), then the ordered pair (K, A) is equal...
- 5x 2 x 2 ,dx is equal to (where c is a constant of integration)
- The equation of a plane containing the line of intersection of the planes 2x - y - 4 = 0 and y + 2z - 4 = 0 and passing through...
- Let y = y(x) be the solution of the differential equation, (x^2+1)^2 dy dx + 2x(x^2+1)y = 1 such that y(0) = 0. If a ,y(1) = 32 ,...
- If f(x) = 2 - x x 2 + x x and g(x) = _e x, (x > 0) then the value of the integral _ - /4 ^ /4 g(f(x)) ,dx is:
- The sum of the squares of the lengths of the chords intercepted on the circle, x^2 + y^2 = 16, by the lines, x + y = n, n ∈ N,...
- The sum of the solutions of the equation | x - 2| + x ( x - 4) + 2 = 0, (x > 0) is equal to:
- The shortest distance between the line y = x and the curve y^2 = x - 2 is:
- The sum of the co-efficients of all even degree terms in x in the expansion of (x + x^3-1 )^6 + (x - x^3-1 )^6, (x > 1) is equal...
- A point on the straight line, 3x + 5y = 15 which is equidistant from the coordinate axes will lie only in:
- Let O(0, 0) and A(0, 1) be two fixed points. Then the locus of a point P such that the perimeter of ΔAOP is 4, is:
- If 2y = ( ^ -1 ( 3 x + x x - 3 x ) )^2, x (0, 2 ) then dy dx is equal to:
- All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in...
- If the tangents on the ellipse 4x^2 + y^2 = 8 at the points (1, 2) and (a, b) are perpendicular to each other, then a^2 is equal...
- _ x 0 ^2x 2 - 1+ x equals:
- If ( + ) = 3 5 , ( - ) = 5 13 and 0 < , < 4 , then tan(2α) is equal to:
- The sum of the series 2 ^ 20 C_0 + 5 ^ 20 C_1 + 8 ^ 20 C_2 + 11 ^ 20 C_3 + + 62 ^ 20 C_ 20 is equal to:
- The length of the perpendicular from the point (2, −1, 4) on the straight line, x+3 10 = y-2 -7 = z 1 is:
- Let f: [0, 2] R be a twice differentiable function such that f''(x) > 0, for all x ∈ (0, 2). If (x) = f(x) + f(2 - x), then φ is:
- The greatest value of c ∈ R for which the system of linear equations x - cy - cz = 0, cx - y + cz = 0, cx + cy - z = 0 has a...